The present invention relates to electric power meters and, more particularly, to a digital power metering apparatus and method.
Electric power is typically generated at a remote, central generating facility and transported to the consumer over a distribution system. To reduce power transportation losses, a step-up, sub-transmission transformer is used to increase the voltage and reduce the current for transmission over a transmission line. The actual transmission line voltage usually depends on the distance between the sub-transmission transformers and the consumers of the electricity but is commonly in the range of 2-35 kilo-volts (“kV”). Distribution substation transformers and distribution transformers of an electric utility's secondary power distribution system reduce the voltage from the transmission line level to a distribution voltage for delivery and use by industrial, commercial, and residential consumers. In the United States, for example, electric power is typically delivered to the consumer as a 60 Hertz (Hz) alternating current voltage (AC) ranging from 120-660 volts (“V”), depending upon the use.
The consumption of power by individual consumers and the performance of the distribution system are monitored by power meters. Power meters are used to monitor a number of electrical parameters related to power distribution and use, including the active power, the time rate of transferring or transforming energy, and the apparent power, the product of the root mean square (RMS) voltage and current. In addition, the reactive power, the product of the RMS voltage and the quadrature component of the current, is commonly monitored to identify capacitive and inductive loads reducing the overall efficiency of the power distribution system. The power factor or quality factor, the ratio of active power to apparent power, is also commonly monitored. The usefulness of monitoring a variety of parameters of electric power has favored adoption of power meters that incorporate digital data processing systems. In a digital power meter, the data processing system uses appropriate mathematical formulas to calculate the various electric power parameters from digital data obtained by sampling transducer outputs that represent, respectively, the voltage and current in a transmission line supplying the load.
As generated, the fundamental AC voltage and current approximate in-phase, 60 Hertz (“Hz”) sine waves over time. Referring to FIG. 1, the effective or true power of the analog sinusoidal voltage 20 and current 22 waveforms is the integral of the product of the instantaneous magnitudes of the voltage and current averaged over a time period, usually a cycle of the waveform:
                    P        =                              1            T                    ⁢                                    ∫              0              T                        ⁢                          (                                                v                  ⁡                                      (                    t                    )                                                  ⁢                                  i                  ⁡                                      (                    t                    )                                                  ⁢                                                                  ⁢                                  ⅆ                  t                                                                                        (        1        )            
where:                P=effective or true power (watts)        v(t)=instantaneous voltage at time t        i(t)=instantaneous current at time t        T=time period, typically a waveform cycle periodIn a digital power meter, the sinusoidal analog voltage 20 and current 22 waveforms are digitally captured by periodically, simultaneously sampling the amplitudes of the outputs of respective voltage and current transducer outputs. The effective power is typically approximated by averaging the sum of the products of the respective instantaneous voltage and current samples for each of the plurality of sampling intervals, for example, the current-voltage product 28, making up at least one cycle of the waveform:        
                              P          ≅                                    1              T                        ⁢                                          ∑                                  k                  =                  1                                                  k                  =                                      T                                          Δ                      ⁢                                                                                          ⁢                      t                                                                                  ⁢                                                v                  ⁡                                      (                    k                    )                                                  ⁢                                  i                  ⁡                                      (                    k                    )                                                  ⁢                                                                  ⁢                Δ                ⁢                                                                  ⁢                t                                                    ⁢                                                      (        2        )            
where:                P=effective power        v(k)=sample voltage for the k-th sample, for example voltage 24        i(k)=sample current for the k-th sample, for example current 26        Δt=sampling interval        
The effective or true power is the actual amount of power being dissipated in the circuit's dissipative elements, usually resistors. While the circuit's reactive elements, capacitors and inductors, do not dissipate significant power, they do produce voltage drops and current draws that reduce the overall efficiency of the power distribution system. Since the voltage drops and current draws of the reactive elements reduce the efficiency of the distribution system, the reactive power is often measured to permit isolating, reducing, and, in some cases, billing the sources producing the inefficiency.
The reactive power (Q) is equal to:
                    Q        ≅                                            sin              ⁢                                                          ⁢              θ                        T                    ⁢                                    ∑                              k                =                1                                            k                =                                  T                                      Δ                    ⁢                                                                                  ⁢                    t                                                                        ⁢                                          v                ⁡                                  (                  k                  )                                            ⁢                              i                ⁡                                  (                  k                  )                                            ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              t                                                          (        3        )            
where:                Q=effective power (VARS)        v(k)=sample voltage for the k-th sample, for example voltage 24        i(k)=sample current for the k-th sample, for example current 26        Δt=sampling interval        θ=phase angleAs generated, the sinusoidal voltage and current waveforms are in-phase, simultaneously reaching zero, maximum, and minimum amplitudes. The phase angle, expressing the temporal relationship of the voltage and current waveforms, is zero and, therefore, the reactive power is zero. If the load is purely resistive, the voltage and current will remain in phase but, if the load is capacitive or inductive, the current waveform will be temporally shifted relative to the voltage waveform so that the waveforms no longer simultaneously attain zero, maximum, and minimum voltage. In the case of a capacitive load, the current waveform is temporally shifted to precede or lead the voltage. On the other hand, if the load is inductive, the current waveform is temporally shifted to lag the voltage. Since inductive and capacitive loads produce a non-zero phase angle 30 or phase, the reactive power will have a non-zero magnitude.        
Sinusoidal waveforms have definite zero crossings and amplitude peaks and, typically, either a zero crossing or an amplitude peak is selected as the distinguishing feature for temporally marking the cycles of the waveform when measuring the phase angle. Referring to FIG. 2C, on the other hand, a substantial portion of the electrical distribution system load comprises electronic loads, including variable speed drives, rectifiers, inverters, and arc furnaces, that draw current 80 in short abrupt pulses 82 rather than in a smooth sinusoidal manner. The impedances of these loads are characterized as non-linear and, when connected to a sinusoidal supply, the current flow is non-sinusoidal and not proportional to the instantaneous voltage. The non-linearity of power electronic loads produce harmonics of the fundamental voltage sine wave.
In a power distribution system, the expected frequency of the voltage or current, e.g., 50 Hz, 60 Hz, or 400 Hz, is conventionally referred to as the “fundamental” frequency, regardless of the actual spectral amplitude peak. Integer multiples of this fundamental frequency are usually referred to as harmonic frequencies or harmonics. Referring to FIGS. 2A and 2B, when a sine wave of the fundamental frequency 20 is combined with a plurality of harmonics 42, 44, 46, 48 the instantaneous amplitude of the resulting waveform 50 is a sum incorporating the instantaneous amplitude of the fundamental waveform and the temporally corresponding instantaneous amplitudes of the harmonic waveforms. Determining the phase of a waveform from an amplitude peak or a zero crossing of a harmonically distorted waveform 50 is problematic because the contributions of higher frequency harmonics commonly produces a plurality of contemporaneous amplitude peaks 52, particularly in the vicinities of the expected amplitude peaks or zero crossings of the fundamental waveform. To determine the phase angle, power meters typically include extensive computational resources for filtering harmonic frequencies or performing other forms of signal processing, such as interpolation, to enable identification of zero crossings or amplitude peaks of harmonically distorted waveforms.
Accurate measurement of electric power also requires compensation for the error introduced by the current transducer of the power meter. Typically, a resistive voltage divider is used to sense the transmission line voltage and a current transformer is used to sense the current flowing in the transmission line. A current transformer typically comprises multiple turns of wire wrapped around the cross-section of a toroidal core. A load current conductor, a transmission line conducting current to the load, is routed through the center of the toroidal current transformer core forming a transformer with single turn primary winding and a multiple turn secondary winding. When current flows in the primary winding, magnetization of the core induces a current in the secondary winding. The secondary winding is commonly connected to an instrument resistor and the flow of current in the instrument resistor produces a voltage that can be used to precisely measure the secondary current providing a basis for calculating the corresponding load current flowing in the conductor that serves as the primary winding. Ideally, the secondary current is precisely equal to the load current in the primary winding divided by the number of turns in the secondary winding:I1=I2(n)  (4)
where:                I1=primary current        I2=secondary current        n=turns ratio.However, actual transformers are not ideal transformers and the magnetization of the core of the current transformer produces errors that affect the accuracy of the readings produced by the meter.        
Current transformer error comprises a phase error and a ratio error. Part of the current in the primary winding is used to magnetize the transformer core with the result that the secondary current is less than the product of the primary current and the ratio of turns in the primary and secondary windings (turn ratio). The ratio error (re) varies with the magnitude of the primary current (I1) as follows:re(%)=K3+K4(log I1)  (5)
where K3 and K4 are constants.
The effect of the ratio error is to alter the relationship between the magnitudes of the measured secondary current (I2) and the primary current (I1) from the theoretical relationship to the relationship:
                              I          1                =                              I            2            ′                    ⁡                      (                          n              +                                                nr                  e                                100                                      )                                              (        6        )            
where I′2=measured secondary current
The magnitude of the measured secondary current (I2′) is related to the theoretical secondary current (I2), as follows:
                              I          2                =                              I            2            ′                    ⁡                      (                          1              +                                                r                  e                                100                                      )                                              (        7        )            
In addition, the magnetization of the transformer core and windings causes a phase shift between the current in the primary winding and the current in the secondary winding. The resulting phase error (pe) varies with the magnitude of the primary current (I1) approximately according to the relationship:pe=K1+K2(I1−M)  (8)
where M, K1 and K2 are constants
In practice M is often approximately equal to ½ and, consequently, a square root approximation can often be conveniently employed as part of the overall correction algorithm.
The values of the constants K1, K2, K3, and K4 depend upon the configuration of the particular current transformer. Factors such as core material and turns ratio affect the values of the constants which are typically ascertained by experimentation with samples of a given core configuration. The values of K1, K2, K3, and K4 are determined for a particular transformer configuration or production batch by comparing the actual performance of a sample of the transformer configuration to the performance of a standard device when the secondary winding is connected in parallel to a particular impedance or burden.
In a typical digital power meter, an instantaneous assumed load current is obtained from the transformer turns ratio and the magnitude of the sample of the secondary current. The assumed load current is used to determine phase and ratio error correction factors that fit the characteristic curves obtained from testing the sample current transformer. The phase and ratio error correction factors are then applied to adjust the assumed load current to obtain the adjusted magnitude of the sample load current. However, a substantial quantity of data must be stored so that appropriate correction factors will be available for all assumed currents within the meter's range or additional data processing resources will be required to calculate the phase and error correction factors whenever a new current sample is processed. In any event, considerable additional data processing resources are required to adjust each sample of the secondary winding current for the phase and error ratio produced by the current transformer.
Accurate power measurement with a digital power meter also requires accurate control of the sampling interval. Sampling and digitizing the voltage and current waveforms is performed by a sampling unit that typically comprises a voltage transducer, a current transducer, and an analog-to-digital converter (ADC) that captures the amplitudes the voltage or current signals at sampling moments and coverts the discrete amplitudes to digital signals of finite precision. In addition, the sampling unit also typically includes a sampling clock to provide a precise sampling interval and one or more digital signal processors (DSP) dedicated to the tasks of initiating sampling and storing the sample values of the voltage and current output by the ADC. Typically, the dedicated DSP polls the ADCs at intervals signaled by the sampling clock to read the magnitude of the voltage or current sample. Providing a dedicated DSP to perform sampling substantially increases the data processing resources and the cost of the sampling unit.
Microprocessors are available with sufficient processing power to perform the sampling of the voltage and current waveforms as well as the other tasks related to the operation of a power meter. While microprocessors are often used to perform a plurality of tasks that may occur coincidently, interrupts are commonly used to determine the order of performance of the various tasks. When an interrupt request is received the microprocessor responds by suspending processing of a lower priority task; storing addresses for the program instructions and any intermediate results of the suspended task; and initiating processing of the interrupt service routine, the program instructions for the higher priority interrupting task. Upon completion of the interrupting task, the microprocessor returns to the interrupted task and, unless a higher priority second interrupt has been received, continues processing the interrupted task. While microprocessors are commonly used to perform multiple tasks, interrupt latency makes combining real time tasks, such as those performed by the sampling unit of a power meter, with the other data processing tasks related to meter operation problematic. Interrupt latency, the interval between the assertion of an interrupt request and the initiation of the interrupt service routine for the asserted interrupt, makes the timing of the initiation of the execution of the interrupt uncertain, making precise timing of real-time tasks, such as sampling, unreliable, and, as a result, potentially making the output of the meter inaccurate.
What is desired, therefore, is a digital data processing system and method for measuring power that combines accurate phase measurement, adjustment for current transformer induced error and reduced data processing hardware requirements.